A Relation on Floer Homology Groups of Homology Handles

Lectures on Floer homology

Floer homology groups in Yang–Mills theory

Floer Homology and Invariants of Homology Cobordism

By using surgery techniques, we compute Floer homology for certain classes of integral homology 3-spheres homology cobordant to zero. We prove that Floer homology is two-periodic for all these manifolds. Based on this fact, we introduce a new integer valued invariant of integral homology 3-spheres. Our computations suggest its homology cobordism invariance.

Floer Homology of Brieskorn Homology Spheres

Every Brieskorn homology sphere (p; q; r) is a double cover of the 3{sphere ramiied over a Montesinos knot k(p; q; r). We relate Floer homology of (p; q; r) to certain invariants of the knot k(p; q; r), among which are the knot signature and the Jones polynomial. We also deene an integer valued invariant of integral homology 3{spheres which agrees with the {invariant of W. Neu-mann and L. Siebe...

Rabinowitz Floer Homology and Symplectic Homology

The first two authors have recently defined RabinowitzFloer homology groups RFH∗(M,W ) associated to an exact embedding of a contact manifold (M, ξ) into a symplectic manifold (W,ω). These depend only on the bounded component V of W \ M . We construct a long exact sequence in which symplectic cohomology of V maps to symplectic homology of V , which in turn maps to Rabinowitz-Floer homology RFH∗...